List questions from vector-spaces

Published on 22 Mar 2026 - 6:19

823

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How to prove the dimension identity of subspace? i.e. $\dim(V_1) + \dim(V_2) = \dim(V_1 + V_2) + \dim(V_1 \cap V_2)$

Published on 22 Mar 2026 - 22:49

104

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if $T$ is isomorphism, how can I prove that $[T^{-1}]_B=[T]_B^{-1}$ for any base $B$ of $V$?

Published on 22 Mar 2026 - 13:16

58

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How can I calculate the formula of $ \dim( N([T]_B))$?

Published on 22 Mar 2026 - 8:02

566

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Prove that the set of linear transformations is a subspace of $Hom(V,V)$

Published on 22 Mar 2026 - 2:32

1.6k

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Is $\{(x,y,z) \in \mathbb{R}^3: 2x+3y+yz=0\}$ a linear subspace of $\mathbb R^3$

Published on 22 Jan 2018 - 19:13

84

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Quotient Spaces and Dimension

Published on 24 Mar 2026 - 11:55

603

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Intersection of Quotient Spaces

Published on 23 Mar 2026 - 20:17

169

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high-level interpretation of the transpose of a vector

Published on 23 Jan 2018 - 7:26

46

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Vectors which combine or sum to a vector contained in a vector space are also in the vector space?

Published on 23 Jan 2018 - 12:07

295

Views

A bijective "isometric" map $T:V \rightarrow V$ preserve inner product.

Published on 21 Mar 2026 - 18:27

143

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Basis of vector spaces in perfect pairing

Published on 20 Mar 2026 - 4:23

65

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Question on quadratic forms of dimension 3

Published on 22 Mar 2026 - 10:05

156

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Finding a basis for V from a list of given vectors

Published on 23 Jan 2018 - 21:20

116

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An examples of a linearly bounded set

Published on 22 Mar 2026 - 12:58

List Question

Intersection of two affine subspaces in vector space

How to prove the dimension identity of subspace? i.e. $\dim(V_1) + \dim(V_2) = \dim(V_1 + V_2) + \dim(V_1 \cap V_2)$

if $T$ is isomorphism, how can I prove that $[T^{-1}]_B=[T]_B^{-1}$ for any base $B$ of $V$?

How can I calculate the formula of $ \dim( N([T]_B))$?

Prove that the set of linear transformations is a subspace of $Hom(V,V)$

Is $\{(x,y,z) \in \mathbb{R}^3: 2x+3y+yz=0\}$ a linear subspace of $\mathbb R^3$

Quotient Spaces and Dimension

Intersection of Quotient Spaces

high-level interpretation of the transpose of a vector

Vectors which combine or sum to a vector contained in a vector space are also in the vector space?

A bijective "isometric" map $T:V \rightarrow V$ preserve inner product.

Basis of vector spaces in perfect pairing

Question on quadratic forms of dimension 3

Finding a basis for V from a list of given vectors

An examples of a linearly bounded set

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